While neither her camp nor the presidency has said whether or not Dlamini-Zuma will continue in her Cabinet post, it is believed that she will not be able to fulfil the two roles adequately.
"It is the prerogative of the president (Jacob Zuma) to decide if the minister will continue in home affairs. We will take our lead from there," Ronnie Mamoepa, Dlamini-Zuma's spokesperson told the Mail & Guardian.
Dlamini-Zuma was elected as the first female head of the AU Commission on Sunday after months of campaigning against incumbent Jean Ping for the position.
The ANC said it would be difficult for Dlamini-Zuma to continue in her current portfolio as home affairs minister.
"As far as we're concerned it's a full-time position at the AU Commission, but it's a government decision so we won't comment on the minister's future," ruling party spokesperson Keith Khoza told the M&G.
Dlamini-Zuma has brought tangible changes to home affairs, previously regarded as a hotbed of corruption and incompetence, a place staffed with government officials who took bribes and slept on the job.
A technocrat at heart, Dlamini-Zuma took over the department in 2009 and immediately got to work.
Building her success on the implementation of effective internal control measures in finance and supply-chain management, Dlamini-Zuma surrounded herself with appropriately skilled individuals and staffed frontline offices with additional personnel to provide services.
Under her watch, the process of applying for official documents was streamlined, to the point where it now takes less than two weeks to apply for and receive an identity document or passport.
The department was subsequently lauded for its outstanding performance in delivering services to citizens, and the department of public service and administration gave Dlamini-Zuma's ministry an award for service excellence and rated it as an employer of choice for 2010 to 2011.
Her department was also awarded its first unqualified audit in 16 years from the auditor general, no mean feat in light of its messy history.
No immediate successors have been earmarked for the role, but the most obvious choice is Dlamini-Zuma's deputy Fatima Chohan, who the minister praised during her tenure for assisting in the department's turnaround.
Nevertheless, Dlamini-Zuma's appointment has left some parties and analysts jittery about the vacuum she leaves behind her.
"We think it's great that Dlamini-Zuma was elected to the AU," DA spokesperson Mmusi Maimane told the M&G on Monday. "But there are concerns as to who her successor will be. Home affairs has delivered incredible results and it will be a tough job to find a suitable individual. "Hopefully it won't be another crony of President Jacob Zuma; we need to the right person to continue her legacy," Maimane added.
But Professor Steven Friedman, director at the University of Johannesburg's Centre for the Study of Democracy, believes it won't be hard to find a replacement.
"Dlamini-Zuma did help to put home affairs on a more productive course, but there is no reason to believe her successor won't carry on in the same vein, ministers don't work alone at the end of the day," said Friedman.
He said the best way forward would be to have a replacement that provides continuity in the department.
"Her replacement must be capable of continuing with her mandate and should send a clear message that there will be no change. If not, there may be problems."